How many objects do you need to spin? I expect you need each one to spin differently - as an "explosion"?
Offhand, I would say that the best (simplest) approach is to start with one object.
To the Rotation parameter (X,Y & Z combined), add an Oscillate behavior.
Set the Wave Shape to Sawtooth and the Speed to 0.
As a recommendation for a starter value, set the Amplitude to 4000.
To the Phase parameter, add a Parameter Behaviors > Ramp.
At the point at which you want the animations to start, set the Start Offset to the frame number of the starting point.
Now... for the End Values.
Starting with the first object's rotation, set the End Value of the Ramp to 2. This will be a "base" value around which you will make variations for each object.
Select the Oscillate and Ramp behaviors of your (first) object and Copy.
Command - shift select all the other objects you want this applied to and Paste. All objects will now have the same rotational behavior.
Now... for each object, vary the End Value of each Ramp by a fraction. Stay within 1.5 to about 4 and every so often (about half the time) use a *negative value* in the same range. This is what will supply the rotational variations over time. [I'm sorry that this might be a tedious task, but I think* it is the best overall option for this kind of effect (I'm open to other suggestions)]. An alternative would be to vary the Amplitudes, but that's a lot more numbers to type than just the "one dot two" numbers for phase... and you will have to type them in — the Phase slides whole numbers and Amplitude maxes at 100.
A brief explanation of Phase:
The Phase parameter in the Oscillate behavior is misleading. The values are whole numbers if you use the slider. However, the Phase is in π radians. If you set the Amplitude to 360º and the Phase to π (3.14159...), the rotational value the behavior applies will be 360º. π/2 (1.570796...) will be 180º, etc.. As you Ramp from 0 to π, that is the number of degrees rotated. Don't be fooled by the "small numbers".
I'll let you work out the implications ;)
HTH